Interpreting Equations

As your students master the meaning of equations, introduce the idea of a variable. The idea that a symbol such as a letter can be part of an equation or expression may take some getting used to. Provide lots of examples.

Ask: What is the value of the left side of the equation 5 +7 = 12? What is the value of the right side?
It is important that students understand that the left side of the equation
equals the right side.

Draw a pan balance on the board. Write "5+7" on one side and "12" on the other.

Ask: Can anyone tell me what equation this picture shows?
Lead them to see that the balance represents the equation 5 + 7 = 12. Remind them that an equation must balance: both sides must be equal.

Next, erase the numbers and write the following equation below the picture: 6 + = 14.

Ask: What number needs to go in the box to make the equation true? How can you tell?
If students have trouble figuring this out, draw six objects on one side of the balance and 14 objects on the other. Ask how many more would be needed to make the scale balance.

Next, erase the box and write an x in its place.

Say: This letter is called a variable. It stands for an unknown number. It works
just like the box. We donít have to use an x. We could use any other letter we
want. Many people use x and y for variables.

Ask: What value for x would make 17 = 10 + x a true mathematical statement?
How do you know?
Be sure to provide ample examples and exercises for students with the variable or box on the right side of the equation as well as the left. You do not want the students to always think the box will appear on one specific side.

Continue with additional examples similar to the previous two.

Continue with additional examples with two addends on each side of the equation. Be sure to place the variable in different positions in the equations.

Wrap-Up and Assessment Hints
Students need significant practice with equations. Assess student progress by asking them with problem sets such as
3 + 8 = 4 + x
3 + x = 4 + 7x + 8 = 4 + 7
3 + 8 = 4 + 7
The goal is for students to understand the concept that the right side of the equation equals the left side and that more than one addend can be present on each side. This is an important concept and worth the extra time to develop it.